简支饱和多孔弹性梁的非线性动力响应  

Nonlinear Dynamical Responses of Simply Supported Saturated Poroelastic Beam

作　　者：杨骁[1] 李丽[2] 

机构地区：[1]上海大学土木工程系,上海200072 [2]上海市应用数学和力学研究所,上海200072

出　　处：《力学季刊》2008年第1期132-136,共5页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(No.10272070);上海市重点学科建设项目(Y0103)

摘　　要：基于饱和多孔弹性梁大挠度变形的数学模型,利用Galerkin截断法,本文研究了两端可渗透的简支饱和多孔弹性梁分别在突加横向均布常载荷和简谐载荷作用下的动力响应,得到了梁弯曲时挠度、弯矩以及孔隙流体压力等效力偶等随时间的响应,考察了不同载荷下多孔弹性梁弯曲的响应特征。结果表明:随着载荷的增加,在常载荷作用下多孔弹性梁非线性大挠度响应与线性小挠度的差别愈加明显,而在简谐载荷作用下,多孔弹性梁的动力响应呈现较丰富的性态,相图由最初的单一椭圆曲线不断变形,形状随载荷幅值的增加而逐渐复杂,同时,时程曲线也由简单正弦曲线变为具有多峰值特征的一个周期曲线。Based on the mathematical model for large deflection of saturated poroelastic beam, the dynami- cal behavior of simply supported saturated poroelastic beam with two permeable ends, subjected to a suddenly applied transversal constant load or a harmonic load, was investigated with Galerkin truncation method. The deflections, bending moments and equivalent couples of pore fluid pressures were obtained, and the characteristics of response for different loads were examined. It shows that, with the load increasing, the differences between the results of nonlinear large deflection model and of the linear small model become more evident for constant load. Furthermore, the dynamical behavior for the harmonic loads is more complicated. The phase disagram changes continually from a single elliptic curve to a complex curve, and, at the same time, the curves of deflection with time change to periodic ones with multi peak values from simple sine curves.

关 键 词：饱和多孔弹性梁 大挠度分析Galerkin截断法 动力响应 

分 类 号：O357.3[理学—流体力学]